Cabinet ministers will discuss possible law changes to what mail can be received and sent by prisoners, after the accused Christchurch gunman was able to send mail to supporters.
The letter, which was sent to a supporter in Russia, was then posted on the website 4chan, which is popular with the alt-right.
This afternoon, in a post-Cabinet press conference, Prime Minister Jacinda Ardern confirmed the Cabinet would be pushing ahead with law changes.
Ms Ardern said the Department of Corrections had raised concerns about the Corrections Act.
"We discussed that the current grounds may not take into account mail being published to a wider audience nor capture broad hate speech and for the need to ensure the law, which was designed in 2004, is fit for purpose," she said.
"We live in an age where the people like the alleged offender in the Christchurch case sought notoriety and that means trying to publish beyond just an individual who a letter may be sent to and we need to make sure the legislation captures that kind of grotesque behaviour," she said.
Ms Ardern said the next step would be for Corrections Minister Kelvin Davis to take these possible changes to a Cabinet committee, within the next fortnight.
She said she wanted to make it clear the letters from the accused gunman should never have been sent in the first place.
"What we need to make sure however, that we have the greatest clarity possible for corrections and ensure there isn't the ability to contest the decisions that are being made by Corrections at the same time," she said.
She added in the meantime, the accused gunman was no longer able to send and receive mail and changes to the system have now been made.
"That means all mail of high concern prisoners will now be checked centrally by a single specialist team, she said.
The prime minister could not give an indication of when a final decision on any possible law changes would be made, as the Cabinet committee may need to seek further information.
Earlier today Corrections chief executive Christine Stevenson accepted its staff could have withheld those letters under the current law.
But she said the legislation could still be improved with "a little bit of a shift" in terminology to allow Corrections to be "a little bit permissive" about what it can block.